The only option is to export package & reports from development environment from cognos connection. This will create a zip file in deployment folder. You need to copy that zip file to deployment folder of production environment and import it from cognos connection of production environment.

There are totally 3 ways in your scenario:
1. Copy report to clipboard, open report from clipboard(make sure your
package is already published in prod environment).
This is feasible if there are fewer reports.
2. Move all your required reports to one folder and export the folder from
Dev environment, and import the same report zip into prod environment(make
sure your package is already published in prod environment).
This is feasible when we have huge set of reports that needs to be
deployed.
3. Export the entire package from dev, and then import the whole package in
Prod(Here we don't have to publish the package)

Export reports and package from Development.
Copy the deployment file from Development to Production
Import the deployment file into Production.

There are a variety of options available in both Import and Export, so make sure you only deploy what you need. Deployment zip files are usually held in cognos-location/deployment but it depends on your Configuration in both environments.

The suggestion to use MotioCi is worth investigating as it simplifies the deployment process and provides historical information, similar to Source Safe.

We have separate file directories for our Development and Production model source. We also have on our workstations separate FM installations that point to our Development and Production environments. When ready to go to production, we copy the source from Development to the Production folder and then publish to the production environment.

As to moving reports, shortcuts and queries, we use CPM Explorer from BrightStar partners. It is a small piece of software that emulates File Explorer and is very easy to use to move the reports. Low cost too!

Dashboard pages are not able to be moved using CPM Explorer so the Cognos Admins recreate these manually.